CN100385459C - Image watermark method based on finite ridgelet transform - Google Patents

Abstract

The present invention relates to an image watermarking method based on finite ridgelet transform, particularly to a finite ridgelet transform theory and an image digital watermarking technique, which belongs to the technical field of information safety. An image is divided into p (which is a prime number) blocks, and a watermark sequence of w={wi wi<; {-1, 1}, 0<=i<=L-1} is generated, wherein the length is L=p-1; next, the finite ridgelet transform is respectively carried our for each block; a direction with maximum energy in a ridgelet field obtained by transformation is searched, and a watermark is embedded in the direction. When the watermark is embedded, a formula with the consideration of the eye sensitivity for different direction changes is utilized, and the embedded strength of the watermark in different directions is different. The same watermark is embedded into each image block, which realizes the localization of the watermark. The image watermarking method provided by the present invention has good watermark invisibility. When the watermark is detected, the discrimination of relative detection values is high. The image watermarking method of the present invention has robustness on general image processing, and especially can resist the image shearing impact.

Description

A kind of image watermark method based on finite ridgelet transform

Technical field

A kind of image watermark method based on finite ridgelet transform belongs to field of information security technology, particularly theoretical the and image digital watermark technology of finite ridgelet transform.

Background technology

Digitizing technique and rapid development of network technology have changed people's life in many aspects.Exchange of multimedia information based on computing machine and network is the use of copyright, the approach that propagation is provided convenience, and copyright is compared with traditional work, has an enormous advantage.Yet the arrival of networked information era has also proposed new challenge to copyright protection, and traditional information encryption can't satisfy the needs of practical application.Digital watermark technology is the application technology of an emerging subject crossing, and it has absorbed the thought and the theory of numerous ambits.Briefly; digital watermark technology is a kind of Information Hiding Techniques; its basic thought is to embed secret information in digital products such as digital picture, Voice ﹠ Video, so that the true and reliable property of the copyright of protection digital product, proof product, follow the tracks of copy right piracy or the additional information of product is provided.Digital watermark technology has become current multi-media information security research field hot spot technology with fastest developing speed, just is being subjected to showing great attention to of international academic community and business circles.Therefore,, carry out research, both had important academic significance, also have very important economic implications digital watermark technology no matter from point of theory or application point.See document for details: J.Cox, L.Miller, A.Bloom, " Digital Watermarking ", Morgan Kaufmann, 2003 and document: Sun Shenghe, Lu Zheming, Niu Xiamu, " digital watermark technology and application ", Science Press, 2004 etc.

The image digital watermark technology is an important research field of digital watermark technology.Since people proposed digital watermark technology from the nineties, image watermark algorithm miscellaneous continued to bring out.More common image watermark embeds algorithm can be divided into three major types:

(1) spatial domain watermarking algorithm.Early stage people are based on spatial domain basically to the research of digital watermarking, and algorithm is simple relatively, and real-time is stronger, but on robustness not as transform-domain algorithm.See document for details: R.G.Van Schyndel, A.Z.Trickle, N.Mee, C.F.Osborne, " A Digital Watermark ", Proceedings of IEEE InternationalConference on Image Processing, 1994,2:86-90 and document: Zhou Lijun, perigene China, Zhi Zheng, " based on the multiple image watermark of m sequence ", Shanghai Communications University's journal, 2001,35 (9): 1317-1320 etc.

(2) DCT territory watermarking algorithm.Discrete cosine transform (DCT) is one of linear transformation the most frequently used in the Digital Signal Processing, and it is that consolidation changes, and has good energy compressed capability and decorrelation ability.Especially, the JPEG compression standard of digital picture is based upon on the DCT basis.Therefore, DCT has been subjected to generally paying attention in the digital watermark processing technology.See document for details: I.J.Cox, J.Kalian, T.Leighton, T.Shamoon, " Secure Spread Spectrum Watermarkingfor Multimedia ", IEEE Trans.on Image Processing.1997,6 (12): 1673-1687 and document: M.A.Suhail, M.S.Obaidat, " Digital Watermarking-based DCT and JPEG Model ", IEEE Trans.onInstrumentation and Measurement, 2003,52 (5): 1640-1647 etc.

(3) the DWT territory embeds algorithm.Wavelet transformation and wavelet analysis are important breakthroughs to Fourier transform and window fourier transform as a kind of mathematical tool, have become data compression, processing and the most useful instrument of analysis.The wavelet transformed domain digital watermark method has the advantage of time-space domain method and dct transform domain method concurrently, is the focus and the most important research direction of current Study of Watermarking.See document for details: A.Lumini, D.Maio, " A Wavelet-based Image WatermarkingScheme ", International Conference on Information Technology:Coding and Computing, March27-29,2000:122-127 and document: S.Tsekeridou, I.Pitas, " Waveleet-based Self-similar Watermarkingfor Still Images ", ISCAS ' 2000, May 28-31,2000,1:220-223 etc.

Wavelet analysis has outstanding performance when handling the one dimension piecewise smooth function, because small echo is good at the singularity of catching zero dimension (point).And to two-dimentional sectionally smooth signal, for example image extensively has the one dimension odd opposite sex, the object edge that for example smooth curve constitutes.Wavelet analysis wire singularity is not a good representational tool.Handle the weakness of higher-dimension situation in order to overcome small echo, Candes and Donoho have proposed a kind of new multi-scale transform---ridge ripple.The ridge ripple can be handled the singularity of lines in the two-dimensional space effectively.Finite ridgelet transform then is a kind of reversible discrete ridgelet transform, compares with other ridgelet transform discretize schemes to have many good qualities.See document for details: E.J.Candes, D.L.Donoho, " Ridgelets:A key tohigher-dimensional intermittency ", Phil.Trans, 1999,2495-2595 and document: Minh.N.Do, MartinVetterli, " The Finite Ridgelet Transform for Image Representation ", IEEE Transactions on ImageProcessing, 2003,12 (1): 16-28 etc.

Summary of the invention

Task of the present invention provides a kind of image watermark algorithm based on finite ridgelet transform, and it has the characteristics of localization watermark, possesses robustness under the routine operation to image.

In order to describe content of the present invention easily, at first some terms are defined.

Define 1. images.The image of mentioning among the present invention all is meant two-dimentional static gray level image.

Define 2. watermarks.Be embedded into the sequence that comprises copyright information in the image.The watermark sequence that uses among the present invention as the scale-of-two bipolar sequence 1,1}.

Defining 3. watermarks embeds.Finger by being embedded into someway in the original image, has obtained embedding the image of watermark with watermark.

Define 4. watermark detection.Finger detects a width of cloth suspect image, judges whether it contains watermark.

Definition 5.FRAT.Limited Radon conversion is the important component part of finite ridgelet transform.Be defined as follows: a real function f is at finite plane Z _p ²On FRAT be defined as:

$r_k\left[l\right]=\mathrm{FRA}{T}_f(k,l)=\frac{1}{\sqrt{p}}\underset{(i,j)\&Element;L_{k,l}}{\mathrm{\&Sigma;}}f[i,j]$

Wherein, L _{K, l}=(i, j): j=ki+l (mod p), i ∈ Z _p, 0≤k≤p, Z _p=0,1 ..., p-1}.

Definition 6.FBP.Limited reflective projection operator is the inverse transformation of limited Radon conversion.Be defined as follows:

${\mathrm{FBP}}_r(i,j)=\frac{1}{\sqrt{p}}\underset{k,l\&Element;P_{i,j}}{\mathrm{\&Sigma;}}{r}_k\left[l\right],(i,j)\&Element;Z_p^2$

Wherein, P _{I, j}=(k, l): l=j-ki (mod p), k ∈ Z _p∪ (p, i) }.

Definition 7.FRAT matrix of coefficients.Matrix to p * p size is done the FRAT conversion, and the matrix that obtains is the FRAT matrix of coefficients.FRAT matrix of coefficients size is (p+1) * p.Wherein, p+1 direction resolved in the capable representative of p+1, and the p row are represented p the coefficient that p displacement correspondence arranged on each direction.

Define 8. one-dimensional discrete wavelet decomposition.The one-dimensional discrete signal is carried out wavelet transform, can decomposite approximate component (low frequency part of representation signal) of ground floor and ground floor details component (HFS of representation signal).Wherein the approximate component of ground floor can continue to be decomposed into approximate component of the second layer and second layer details component again, and the rest may be inferred.

Define 9. finite ridgelet transforms.Earlier the matrix in the spatial domain is FRAT, obtains the FRAT matrix of coefficients, again each row sequence of FRAT matrix of coefficients is done the one-dimensional discrete wavelet transformation.Whole process is a finite ridgelet transform just.

Define 10. related coefficients.Here refer to cross-correlation coefficient, characterize the degree of correlation of two signals.Its value is between [1,1].Related coefficient is big more, and the similarity degree of two signals of expression is big more.

Define 11. detection thresholds.Judge the threshold value whether watermark exists.

Definition 12.PSNR.Y-PSNR.A kind of method of testing of the measurement picture quality based on pixel.

Detailed technology scheme of the present invention is:

A kind of image watermark method based on finite ridgelet transform comprises watermark embedding and watermark detection process, it is characterized in that, described watermark embed process comprises the following step:

Step 1, watermark sequence w={w that length is L=p-1 (p is a prime number) of generation _i| w _i∈ 1,1}, 0≤i≤L-1}.

Step 2, the selected block size p (p=L+1) that divides carry out piecemeal to original image I, establish to be divided into N piecemeal altogether, promptly obtain block image B _x, 0≤x≤N-1.

Step 3, to each block image, carry out following operation:

Step 3-1, to block image B _x, 0≤x≤N-1 does the FRAT conversion, obtains the FRAT matrix of coefficients R of (p+1) * p size _x, 0≤x≤N-1.

Step 3-2, to FRAT matrix of coefficients R _xEach the row do the one-dimensional discrete wavelet decomposition, obtain ground floor details vector sequence d _{X, k}, 0≤x≤N-1,0≤k≤p.

Step 3-3, sequence of calculation d _{X, k}Energy e _{Z, k},

$e_{x,k}=\frac{1}{p-1}\underset{i=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{d}_{x,k,i}^2$

Step 3-4, preset parameter x find out e _{X, k}A middle maximum e _{X, m}, corresponding details vector sequence is d _{X, m}

Step 3-5, watermark is embedded into sequence d by following formula _{X, m}In,

d′ _x，m，i＝d _x，m，i+α _mβw _i，0≤i≤p-2

Wherein, α _mBe the orientation-sensitive factor, it has reflected the sensitivity of human eye to different directions.β is the self adaptive pantographic factor, by d _{X, m, i}Value decision, can adopt following polygronal function to decide β:

$\left\{\begin{array}{cc}\mathrm{\&beta;}=b,& \left|d_{x,m,i}\right|\&le;a\\ \mathrm{\&beta;}=\frac{b}{a}\left|d_{x,m,i}\right|,& \left|d_{x,m,i}\right|>a\end{array}\right.$

Wherein, a, b (a＞0, b＞0) are the artificial constants of setting.

Step 3-6, according to above step, obtain the FRAT matrix of coefficients R ' behind the embed watermark _x, it is FBP, obtain the block image B ' of embed watermark _x

Step 4, with the block image B ' of all embed watermarks _x, be stitched together again, just obtain the image I of embed watermark.

Described watermark detection process comprises the following step:

Step 1, the call parameter when knowing the watermark embedding.Comprise branch block size p and watermark sequence w etc.

Step 2, with image I to be detected ' be divided into N piecemeal, block image is: C _x, 0≤x≤N-1.

Step 3, to each piecemeal, carry out following operation:

Step 3-1, to block image C _x, 0≤x≤N-1 does the FRAT conversion, obtains the FRAT matrix of coefficients W of (p+1) * p size _x, 0≤x≤N-1.

Step 3-2, to FRAT matrix of coefficients W _xEach the row do the one-dimensional discrete wavelet decomposition, obtain ground floor details vector sequence d ' _{X, k}, 0≤x≤N-1,0≤k≤p.

Step 3-3, sequence of calculation d ' _{X, k}Energy e ' _{X, k},

$e_{x,k}^{\&prime;}=\frac{1}{p-1}\underset{i=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{d}_{x,k,i}^{\&prime;2};$

Step 3-4, preset parameter x find out e ' _{X, k}A middle maximum e ' _{X, m}, corresponding details vector sequence is d ' _{X, m}, the position of promptly having found watermark to embed.

Step 3-5, sequence of calculation d ' _{X, m}With the related coefficient of watermark sequence w,

$z_x=\frac{\underset{i}{\mathrm{\&Sigma;}}{d}_{x,m,i}^{\&prime;}{w}_i}{\sqrt{\underset{i}{\mathrm{\&Sigma;}}{d}_{x,m,i}^{\&prime;2}\underset{i}{\mathrm{\&Sigma;}}{w}_i^2}},0\&le;i\&le;p-2$

Step 4, the related coefficient z that all piecemeals are obtained _x, it is one average that 0≤x≤N-1 does, and obtains the related coefficient z of entire image and watermark.

Step 5, setting detection threshold z _t, and judge: if z＜z _t, the process decision chart picture does not contain watermark; If z 〉=z _t, process decision chart looks like to contain watermark.

In the such scheme, divide block size p to equal 17 described in the step 2.

Need to prove:

1. require in the telescopiny step 2 to divide the selected of block size, p is a prime number, and this is necessary.Because the matrix of FRAT requirement carrying out conversion must be that p * p size and p are prime number.Because be subjected to the restriction of FRAT and this embedding algorithm, the watermark sequence length of Qian Ruing can only be p here.

2. image being carried out the reason that piecemeal handles is: finite ridgelet transform only is suitable for handling straight line of image, and the curve lines in the real world images exist more generally than straight line lines.If directly entire image is made finite ridgelet transform, the result after the conversion is coarse and inaccurate to the sign of linear feature so.So similar many DCT territory watermarking algorithm will be divided into image some fritters earlier in the present invention.After the piecemeal, the curve lines just can go to approach with straight line in each fritter approx.

3. find out a details vector sequence of energy maximum, watermark is embedded into the there.This is because a direction of linear feature is arranged in the common corresponding spatial domain of a details vector sequence of energy maximum most, also is that image texture changes abundant zone in the spatial domain.Watermark is embedded into these zones to be difficult for being discovered by human eye.On the other hand, only select a direction embed watermark can improve the efficient and the real-time of algorithm.

4. human eye is to the susceptibility difference of different directions.The variation of vertical and horizontal direction is just compared vergence direction the variation sensitivity many.Variation vertical and horizontal direction is discovered owing to being easy to cause, so when looking for the details component of energy maximum, the sequence of this both direction can be foreclosed.

5. the broken line that adopts among the telescopiny step 3-5 embeds rule and is actually addition criterion and the multiplication criterion that combines the watermark embedding.Obtain high linear correlation values when adopting the addition criterion to be beneficial to watermark detection, and adopt the multiplication criterion can realize the adaptivity that watermark embeds, and better robustness is arranged.

Innovation part of the present invention is:

1. finite ridgelet transform is applied in the digital watermarking algorithm.Finite ridgelet transform is emerging in recent years a kind of method, and it has obtained good effect at linear feature detection and image noise reduction and recovery field, but its document that combines with digital watermark technology is also very rare.

2. search a details vector sequence of FRAT matrix of coefficients energy maximum, only watermark is embedded into the there.Both guaranteed that watermark was embedded in the important area of image (possessing line feature or texture variations complexity), and the complexity of embedding algorithm and detection algorithm is not high yet.

3. same watermark is embedded in a plurality of piecemeals of image.So on the one hand the robustness of algorithm is improved greatly, make watermark detection can only detect one or several piecemeal on the other hand, improve the speed of testing process.More importantly, the method for this localization watermark can be resisted the attack of cutting out to image, is promptly cutting out an image from the image of embed watermark, because it has still comprised several complete piecemeals, exists so can detect watermark.

4. include the orientation-sensitive factor in the formula of embed watermark, can adjust the watermark embed strength on the different directions in conjunction with the varying sensitivity of human eye to the different directions variation.

5. the broken line rule that adopts during embed watermark.The broken line rule combines the addition criterion of watermark embedding and the advantage of multiplication criterion, can make watermark embed strength find a good equilibrium point between robustness and invisibility.

Description of drawings

Fig. 1 is the schematic flow sheet of watermark embed process of the present invention.

Fig. 2 is the schematic flow sheet of watermark detection process of the present invention.

Specific embodiment

Adopt method of the present invention, use Matlab or C language to realize the program of watermark embedding and watermark detection.The image of testing 256 gray levels of selecting 256 * 256 sizes for use divides block size p=17 as test pattern, and the one-dimensional discrete small echo is selected the Daubechies-4 small echo for use, and the embedding parameter is α _k=1, a=10, b=2.Detection threshold is set at 0.035.Produce 100 watermarks at random, divide to embed in the original image for 100 times, obtain 100 watermarking images that contain that embed different watermarks.These images are done conventional processing, add up their false dismissal probabilities, see the following form watermark detection:

The Flame Image Process of carrying out	False dismissal probability
		Do not handle	0％
Add Gauss's noise (average 0,8 gray-scale values of standard deviation)	0％
		3 * 3 medium filterings	11％
JPEG compresses (quality factor 75%)	7％
		Cut out at random	26％

In sum, watermarking algorithm provided by the invention has made full use of the characteristic of finite ridgelet transform, the method novelty, and possess robustness preferably, certain practical value is arranged.

Claims (3)

1. the image watermark method based on finite ridgelet transform comprises watermark embedding and watermark detection process, it is characterized in that, described watermark embed process comprises the following step:

Step 1, to produce a length be L=p-1, and p is a prime number, watermark sequence w={w _i| w _i∈ 1,1}, 0≤i≤L-1};

Step 2, the selected block size p that divides, p=L+1 carries out piecemeal to original image I, establishes to be divided into N piecemeal altogether, promptly obtains block image B _x, 0≤x≤N-1;

Step 3, to each block image, carry out following operation:

Step 3-1, to block image B _x, 0≤x≤N-1 does the FRAT conversion, obtains the FRAT matrix of coefficients R of (p+1) * p size _x, 0≤x≤N-1;

Step 3-2, to FRAT matrix of coefficients R _xEach the row do the one-dimensional discrete wavelet decomposition, obtain ground floor details vector sequence d _x, k, 0≤x≤N-1,0≤k≤p;

Step 3-3, sequence of calculation d _{X, k}Energy e _{X, k},

$e_{x,k}=\frac{1}{p-1}\underset{i=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{d}_{x,k,i}^2;$

Step 3-4, preset parameter x find out e _{X, k}A middle maximum e _{X, m}, corresponding details vector sequence is d _{X, m}

Step 3-5, watermark is embedded into sequence d by following formula _{X, m}In,

d _x，m，i′＝d _x，m，i+α _mβw _i，0≤i≤p-2，

Wherein, α _mBe the orientation-sensitive factor, β is the self adaptive pantographic factor, by d _{X, m, i}Value decision, can adopt following polygronal function to decide β:

$\left\{\begin{array}{cc}\mathrm{\&beta;}=b,& \left|d_{x,m,i}\right|\&le;a\\ \mathrm{\&beta;}=\frac{b}{a}\left|d_{x,m,i}\right|,& \left|d_{x,m,i}\right|>a\end{array}\right.$

Wherein, a, b are the artificial constants of setting, and a＞0, b＞0;

Step 3-6, according to above step, obtain the FRAT matrix of coefficients R behind the embed watermark _x', it is FBP, obtain the block image B of embed watermark _x';

Step 4, with the block image B of all embed watermarks _x', be stitched together again, just obtain the image I of embed watermark;

Described watermark detection process comprises the following step:

Step 5, the call parameter when knowing the watermark embedding comprise branch block size p and watermark sequence w;

Step 6, with image I to be detected ' be divided into N piecemeal, block image is: C _x, 0≤x≤N-1;

Step 7, to each block image, carry out following operation:

Step 7-1, to block image C _x, 0≤x≤N-1 does the FRAT conversion, obtains the FRAT matrix of coefficients W of (p+1) * p size _x, 0≤x≤N-1;

Step 7-2, to FRAT matrix of coefficients W _xEach the row do the one-dimensional discrete wavelet decomposition, obtain ground floor details vector sequence d _{X, k}', 0≤x≤N-1,0≤k≤p;

Step 7-3, sequence of calculation d _{X, k}' energy e _{X, k}',

$e_{x,k}^{\&prime;}=\frac{1}{p-1}\underset{i=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{d}_{x,k,i}^{\&prime;2};$

Step 7-4, preset parameter x find out e _{X, k}An e of ' middle maximum _{X, m}', corresponding details vector sequence is d _{X, m}', the position of promptly having found watermark to embed;

Step 7-5, sequence of calculation d _{X, m}' with the related coefficient of watermark sequence w,

$z_x=\frac{\underset{i}{\mathrm{\&Sigma;}}{d}_{x,m,i}^{\&prime;}{w}_i}{\sqrt{\underset{i}{\mathrm{\&Sigma;}}{d}_{x,m,i}^{\&prime;2}\underset{i}{\mathrm{\&Sigma;}}{w}_i^2}},$ 0≤i≤p-2；

Step 8, the related coefficient z that all piecemeals are obtained _x, it is one average that 0≤x≤N-1 does, and obtains the related coefficient z of entire image and watermark;

Step 9, setting detection threshold z _t, and judge: if z＜z _t, the process decision chart picture does not contain watermark; If z 〉=z _t, process decision chart looks like to contain watermark.

2. a kind of image watermark method based on finite ridgelet transform according to claim 1 is characterized in that, divides block size p to equal 17 described in the step 2.

3. a kind of image watermark method according to claim 1 based on finite ridgelet transform, it is characterized in that the one-dimensional discrete small echo is selected the Daubechies-4 small echo for use described in the step 3-2 of described watermark embed process and the step 7-2 of described watermark detection process; Orientation-sensitive factor-alpha described in the step 3-5 of described watermark embed process _m=1, described constant a=10, b=2; The z of detection threshold described in the step 9 of described watermark detection process _tBe set at 0.035.